Monte Carlo methods are used to model phenomena with significant uncertainty in inputs, such as the calculation of risk in business. When Monte Carlo simulations have been applied in pro-forma business estimates their predictions of profit and profit margin are routinely better than human intuition or alternative "soft" methods.
Profit risk is determined by a number of factors that each have their own statistical distribution. By calculating the overall risk thousands of times using randomly generated values within the statistical distribution of each input, Monte Carlo simulation generates a probability distribution for the overall profit risk. That distribution can be easily understood when displayed as a graph.
For example, the profit of a new product offering in a restaurant may depend on the cost of ingredients, additional labor and equipment, as well as expected number of units sold and the price. Conventional profit estimates might be based on an equation with those inputs to predict a best and a worst case, though the probability of either best or worst case is small. Monte Carlo simulation would present a probability between the best and worst cases. The probability of making any particular profit can be read directly from a chart. In the example – the predicted profitability of a new product offering – there is a nearly 95% probability of achieving at least a four thousand dollar profit on that new offering.
Monte Carlo methods vary, but for pro forma calculations tend to follow a particular pattern:
- Determine a predictive equation for profit.
- Define a domain of inputs into that equation.
- Generate inputs randomly from a probability distribution over the domain.
- Compute the results of the predictive equation for each set of randomly generated inputs.
- Aggregate the results into a graph.